List of top Mathematics Questions on Set Theory

Let S = {1, 2, 3, 4, 5, 6} and X be the set of all relations R from S to S that satisfy both the following properties :
i. R has exactly 6 elements.
ii. For each (a, b) ∈ R, we have |a - b| ≥ 2.
Let Y = {R ∈ X : The range of R has exactly one element} and
Z = {R ∈ X : R is a function from S to S}.
Let n(A) denote the number of elements in a set A.

Match List - I with List - II.

List - I	List -II
(A) \(P(\overline{A} \cap B)\)	(I)\(P(A)+P(B)\)
(B)\(P(A\cap \overline B)\)	(II)\(P(A)+P(B)-2P(A\cap B)\)
(C) \(P[(A\cap \overline B) \cup (\overline A \cap B)]\)	(III)\(P(B)-P(A\cap B)\)
(D)\(P(A\cup B)+ P(A\cap B)]\)	(IV)\(P(B)-P(A\cap B)\)

Choose the correct answer from the options given below:

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